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Intelligent reflecting surfaces (IRSs) are a promising low-cost solution forachieving high spectral and energy efficiency in future communication systemsby enabling the customization of wireless propagation environments. Despite theplethora of research on resource allocation design for IRS-assisted multiusercommunication systems, the optimal design and the corresponding performanceupper bound are still not fully understood. To bridge this gap in knowledge, inthis paper, we investigate the optimal resource allocation design forIRS-assisted multiuser systems employing practical discrete IRS phase shifters.In particular, we jointly optimize the beamforming vector at the base station(BS) and the discrete IRS phase shifts to minimize the total transmit power forthe cases of perfect and imperfect channel state information (CSI) knowledge.To this end, two novel algorithms based on the generalized Bendersdecomposition (GBD) method are developed to obtain the globally optimalsolution for perfect and imperfect CSI, respectively. Moreover, to facilitatepractical implementation, we propose two corresponding low-complexitysuboptimal algorithms with guaranteed convergence by capitalizing on successiveconvex approximation (SCA). In particular, for imperfect CSI, we adopt abounded error model to characterize the CSI uncertainty and propose a newtransformation to convexify the robust quality-of-service (QoS) constraints.Our numerical results confirm the optimality of the proposed GBD-basedalgorithms for the considered system for both perfect and imperfect CSI.Furthermore, we unveil that both proposed SCA-based algorithms can achieve aclose-to-optimal performance within a few iterations. Moreover, compared withthe state-of-the-art solution based on the alternating optimization (AO)method, the proposed SCA-based scheme achieves a significant performance gainwith low complexity.

Globally Optimal Resource Allocation Design for Discrete Phase Shift IRS-Assisted Multiuser Networks with Perfect and Imperfect CSI